Is it permissible to bury new deceased family members in unidentified graves within the family's plot in the cemetery, knowing that the cemetery is overcrowded and the authorities do not allow new graves to be opened except by burying one person on top of another in old graves?

The basic rule is that it is impermissible to exhume a grave to bury another deceased person unless there is a necessity. So, if the competent authorities prohibit burial except in specific graves, then it is permissible to exhume them and bury in them. There is no harm in burying in graves that do not belong to your family when there is a necessity; otherwise, it is not permissible. It appears that the land is owned by you, unless another person claims ownership of it with evidence, in which case it is not permissible to bury in it except with their permission.